Nonsmooth H∞ synthesis of non-minimum-phase servo-systems with backlash

Abstract The nonsmooth phenomena such as backlash and Coulomb friction, often occurring in mechanical systems, typically produce undesired inaccuracies, oscillations and instability thereby degrading the system performance. The present paper addresses these phenomena in a benchmark two-mass system composed of motor and load subsystems joined by an elastic shaft. Only partial measurements of the motor position are assumed to be available. The H ∞ synthesis is then developed for a class of nonsmooth systems with backlash. The effectiveness of the proposed synthesis and its robustness features in the presence of friction forces and backlash effects are supported by an experimental study made for an industrial emulator.

[1]  Bo Egardt,et al.  Backlash Estimation With Application to Automotive Powertrains , 2007, IEEE Transactions on Control Systems Technology.

[2]  San Nicol,et al.  Analysis of PD and Nonlinear Control of Mechanical Systems with Dynamic Backlash , 2002 .

[3]  Ying Zhang,et al.  Adaptive backstepping control of a class of uncertain nonlinear systems with unknown backlash-like hysteresis , 2004, IEEE Trans. Autom. Control..

[4]  L. P. Khoo,et al.  A novel algorithm to generate backlash-free motions , 2010 .

[5]  Haibo Zhao.  Backstepping adaptive control of dual-motor driving servo system with backlash nonlinearity , 2013, 2013 Fourth International Conference on Intelligent Control and Information Processing (ICICIP).

[6]  A. Isidori,et al.  Disturbance attenuation and H/sub infinity /-control via measurement feedback in nonlinear systems , 1992 .

[7]  Xinkai Chen,et al.  Modeling and inverse adaptive control of asymmetric hysteresis systems with applications to magnetostrictive actuator , 2014 .

[8]  Rochdi Merzouki,et al.  Compensation of friction and backlash effects in an electrical actuator , 2004 .

[9]  Bo Egardt,et al.  Estimation of backlash with application to automotive powertrains , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[10]  G. Agranovich,et al.  Backlash compensation for motion system with elastic transmission , 2012, 2012 IEEE 27th Convention of Electrical and Electronics Engineers in Israel.

[11]  Shaocheng Tong,et al.  Adaptive Fuzzy Control for a Class of Nonlinear Discrete-Time Systems With Backlash , 2014, IEEE Transactions on Fuzzy Systems.

[12]  Chun-Yi Su,et al.  Robust adaptive control of a class of nonlinear systems with unknown backlash-like hysteresis , 2000, IEEE Trans. Autom. Control..

[13]  Xu Feng,et al.  Fuzzy control of a nonlinear pointing testbed with backlash and friction , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[14]  Gang Tao,et al.  Adaptive control of systems with backlash , 1993, Autom..

[15]  B. Brogliato,et al.  Analysis of Proportional—Derivative and Nonlinear Control of Mechanical Systems with Dynamic Backlash , 2003 .

[16]  M. Grundelius,et al.  Adaptive control of systems with backlash acting on the input , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[18]  Yury Orlov,et al.  Generic Nonsmooth $\mathcal {H}_{\infty }$ Output Synthesis: Application to a Coal-Fired Boiler/Turbine Unit With Actuator Dead Zone , 2015, IEEE Transactions on Control Systems Technology.

[19]  Mattias Nordin,et al.  Controlling mechanical systems with backlash - a survey , 2002, Autom..

[20]  Yury Orlov,et al.  Nonlinear H∞-Output Regulation of a Nonminimum Phase Servomechanism With Backlash , 2007 .

[21]  Bo Mo,et al.  The adaptive PID controller design for motor control system with backlash , 2013, 2013 Fourth International Conference on Intelligent Control and Information Processing (ICICIP).

[22]  Bernard Friedland,et al.  Feedback control of systems with parasitic effects , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[23]  William P. Heath,et al.  Controller structure for plants with combined saturation and deadzone/backlash , 2012, 2012 IEEE International Conference on Control Applications.

[24]  Zhi Liu,et al.  Fuzzy adaptive control of nonlinear uncertain plants with unknown dead zone output , 2015, Fuzzy Sets Syst..

[25]  H. Mokhtari,et al.  A New Scheme for a Mechanical Load Position Control Driven by a Permanent Magnet DC Motor and a Nonzero Backlash Gearbox , 2006, 2006 IEEE International Symposium on Industrial Electronics.

[26]  Leonardo Acho,et al.  Robust Control Design for Mechanisms with Backlash , 2013 .

[27]  Y. Orlov.  Discontinuous Systems: Lyapunov Analysis and Robust Synthesis under Uncertainty Conditions , 2008 .

[28]  Yury Orlov,et al.  Sensorless Nonsmooth H∞-Tracking Synthesis of Servosystems with Backlash and Coulomb Friction∗ , 2015 .

[29]  Yong-Hua Liu,et al.  Global adaptive control for uncertain nonaffine nonlinear hysteretic systems. , 2015, ISA transactions.

[30]  A. Schaft.  L/sub 2/-gain analysis of nonlinear systems and nonlinear state-feedback H/sub infinity / control , 1992 .

[31]  Maria Letizia Corradini,et al.  Robust stabilization of nonlinear uncertain plants with backlash or dead zone in the actuator , 2002, IEEE Trans. Control. Syst. Technol..

[32]  Yury Orlov,et al.  Robust tracking control of servo systems with backlash: Nonsmooth ℋ∞ control vs. linear ℋ∞ control , 2015, 2015 American Control Conference (ACC).

[33]  Béla Lantos,et al.  Control of mechanical systems with Stribeck friction and backlash , 2009, Syst. Control. Lett..

[34]  Yury Orlov,et al.  Switched chattering control vs. backlash/friction phenomena in electrical servo-motors , 2003 .

[35]  T. Basar,et al.  H∞-0ptimal Control and Related Minimax Design Problems: A Dynamic Game Approach , 1996, IEEE Trans. Autom. Control..

[36]  Y. Nakayama,et al.  A torque control method of three-inertia torsional system with backlash , 2000, 6th International Workshop on Advanced Motion Control. Proceedings (Cat. No.00TH8494).

[37]  E. A. Freeman.  The effect of speed-dependent friction and backlash on the stability of automatic control systems , 1959, Transactions of the American Institute of Electrical Engineers, Part II: Applications and Industry.

[38]  Per-Olof Gutman,et al.  New models for backlash and gear play , 1997 .